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A source of oxygen could easily made burn on Neptune, like a source of hydrogen on Earth.
Or take a sample of Neptun's atmosphere. It would easily burn in Earth's atmosphere.

Hydrogen oxygen combustion is sufficiently exothermic (483.6 kJ/mol of O2) to sustain burning even at the low temperatures on Neptune, provided the atmospheric pressure is high enough: With a gas constant of about 8.3 J / mol K, the gas can easily be heated up to the point of combustion by the energy released by the combustion.

Assuming oxygen would be provided, just sufficiently to burn up hydrogen and trace hydrocarbons:
After the explosion and condensation Neptune would get a huge ocean of water, later freezing to water ice, with an atmosphere of helium, and some less abundant gases like CO2, nitrogen, and argon, traces of water vapor. Traces of hydrogen and methane could survive the presence of oxygen. Hence some oxygen would remain in the atmosphere. Most of the CO2 would be resolved in the water ice.

The average density of Neptune would increase, it would shrink a bit, the core would be compressed and heated by adiabatic compression.

Before combustion Neptune's gravity is strong enough to hold an atmosphere of hydrogen, the easiest gas to escape. Hence the denser planet after combustion wouldn't improve its capability to keep an atmosphere significantly: The escape velocity of Neptune is 23.5 km/s, its surface temperature is below 100K. With Boltzmann constant $k=1.38\cdot 10^{-23}J/K$ and $E=3kT/2$ we get $$E=3\cdot 1.38\cdot 10^{-23}J/K\mbox{ or }4.14\cdot 10^{-21}J\mbox{ at }100K$$ for an average $H_2$ molecule with a mass of about $3.35\cdot 10^{-27}kg$. Hence for Neptun's escape velocity the kinetic energy of a hydrogen molecule is $$E=0.5\ mv^2=0.5\cdot 3.35\cdot 10^{-27}kg \cdot (23.5\cdot 10^3 m/s)^2 = 9.25\cdot 10^{-19} J.$$ Hence the energy needed to escape is more than 200-times the kinetic energy of the hydrogen molecules; no way to escape, 2000K or more would be needed to let escape some hydrogen over time (to get below a factor of about ten between the two energies). Photolyic dissociated atomic hydrogen would still need more than 1000K to escape.

The probability to catch asteroids or comets would be reduced due to the reduced radius, if the total mass is adjusted to the mass before combustion, since asteroids would miss instead of hit the planet.

Excellent, thank you very much.. Another matter I hope you could add to your answer; Would neptune start now to collect gases again as the gravity now would be significantly larger at the surface and this new planet would act as it's core?
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YodaFeb 4 '14 at 21:25

I don't understand "why" about what I'm afraid. But I guess you are asking about the gravity at the surface. I have assumed that because as the planet shrinks and become more dense, the surface will be more closer to the center of gravity. Ofcourse I assume the mass wouldn't change, so overall gravity would remain the same. If that's not the question, please clarify.
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YodaFeb 4 '14 at 22:40